SOLUTION: A student is taking a​ multiple-choice exam in which each question has four choices. Assuming that she has no knowledge of the correct answers to any of the​ questions, she has

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Question 1190719: A student is taking a​ multiple-choice exam in which each question has four choices. Assuming that she has no knowledge of the correct answers to any of the​ questions, she has decided on a strategy in which she will place four balls​ (marked A,B,C,D ​) into a box. She randomly selects one ball for each question and replaces the ball in the box. The marking on the ball will determine her answer to the question. There are six ​multiple-choice questions on the exam.
What is the probability that she will get at least five questions​ correct?
Answer by ikleyn(53937) About Me  (Show Source):
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A student is taking a​ multiple-choice exam in which each question has four choices.
Assuming that she has no knowledge of the correct answers to any of the​ questions,
she has decided on a strategy in which she will place four balls​ (marked A,B,C,D ​) into a box.
She randomly selects one ball for each question and replaces the ball in the box.
The marking on the ball will determine her answer to the question.
There are six ​multiple-choice questions on the exam.
What is the probability that she will get at least five questions​ correct?
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This many-words description means simple thing: for any multiple-choice question,
the answer is selected randomly among four possibilities;

so, the probability of getting a correct answer is  1%2F4 = 0.25, while the probabiliy 
of getting incorrect answer is  3%2F4 = 0.75  for each single multiple choice question.


And the answers to different multiple-choice questions are independent each from another.


It is a typical binomial distribution situation. The formula for the probability to get 5 or more correct answers is

    P = P(5) + P(6) = C%5B6%5D%5E5%2A0.25%5E5%2A0.75%5E1 + C%5B6%5D%5E6%2A0.25%5E6%2A0.75%5E0 = 

                      6%2A0.25%5E5%2A0.75+%2B+0.25%5E6 = 0.004639.    ANSWER

Solved.

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To see many other similar  (and different)  solved problems,  look into the lessons
    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems
in this site.